P-, Q-, AND R-TECHNIQUES 175

calculation. What the requirements are may be gathered from my
discussion on the postulates of measurement in the preceding
section.

Difference of Aim.—Where the preliminary process of
averaging or ranking by persons is legitimate, it is evident
that it must automatically eliminate from further considera-
tion any differences in average or general level that dis-
tinguish one person from another. Thus, if we wish to
know whether finger-length varies with height, we ignore
the fact that fingers are small objects and statures large
objects, the difference in the absolute size of the two traits
being irrelevant to the comparison. Similarly, if we wish
to know whether the proportions of the dwarf correspond
with those of the normal adult, we ignore the difference in
body-bulk of the two persons. And generally, in correlat-
ing traits, we virtually eliminate the general factor that
would have been obtained by correlating persons; and, in
correlating persons, we virtually eliminate the general
factor that would have been obtained by correlating traits.
Even if we do not actually * standardize ' the measurements,
i.e. if we rely on covariances or product-moments, we are
still forced to deal with deviations or with differences, that
is, with relative measurements, not with absolute; and that
means that with either procedure we still discard a factor
that the alternative procedure would preserve, namely, the
so-called general factor. In my view, however, this is the
only essential difference between the two sets of factors derived
by the two opposite procedures. The remaining factors
(the subordinate, ' bipolar,' c group-,' or ' type-' factors)
will in theory be essentially the same whether we start by
correlating persons or by correlating traits.

If this view be correct, the difference between the two
modes of approach lies rather in a difference of aim or
interest than in a difference of technique. We may cor-
relate persons for one or other of two reasons. First, we
may be interested in the general factor for persons, and prefer
to investigate this on the basis of a weighted average rather
than an unweighted.1 Secondly, we may be interested, not

1 An explicit example may make this clearer to those who are not already
familiar with the general procedure. In the Binet-Simon tests the scheme of